#91273

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

Hall	C₃×C₅ ⋊ #135
Sylow	C₅ ⋊ #912
Sylow	C₃ ⋊ #4050

Subgroups

	subgroup	G/H
center	C₂	D₃×D₂₀
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂×D₃×D₅
Fitting	C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₈	D₃×D₅
hypocenter	C₃×C₅	#135
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,4,5,3)(6,7,8)(9,12,11,18,14,21,13,20)(10,16,22,24,17,23,15,19);(7,8)(9,11,14,13)(10,15,17,22)(12,18,21,20)(16,19,23,24);(2,3)(4,5)(9,10)(11,15)(12,19)(13,22)(14,17)(16,20)(18,23)(21,24)

Polycyclic presentation:

2^5,3,5|b^2=e,c^2=de,d^2=e,c^a=cd,d^a=de,g^a=g^4,f^b=f^2

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746820, #11746835, #11746836, …
maximal normal subgroup of	#11746820, #11746835, #11746836, …
maximal quotient of	#11747682, #11747683, #11747739, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 349);